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Which condition between \(b\) and \(c\) is necessary for the trinomial \(x^2+bx+c\) to be identified as a perfect-square trinomial?
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Answer and explanation
Correct answer: \(c=\left(\frac{b}{2}\right)^2\)
A perfect-square trinomial has the form \((x+k)^2=x^2+2kx+k^2\). Thus \(b=2k\), so \(k=\frac{b}{2}\) and \(c=k^2=\left(\frac{b}{2}\right)^2\). Exam tip: halve the middle coefficient and square it to check the constant term.
Frequently asked questions
What is the correct answer to this question?
\(c=\left(\frac{b}{2}\right)^2\)
Why is this the correct answer?
A perfect-square trinomial has the form \((x+k)^2=x^2+2kx+k^2\). Thus \(b=2k\), so \(k=\frac{b}{2}\) and \(c=k^2=\left(\frac{b}{2}\right)^2\). Exam tip: halve the middle coefficient and square it to check the constant term.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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